对B.M.Brown等人提出的开问题的探讨

数学物理学报 ›› 2013, Vol. 33 ›› Issue (4): 709-718.

对B.M.Brown等人提出的开问题的探讨

景海斌¹|王欣阵²|綦建刚³

1.河北建筑工程学院数理系河北张家口 075000|2.浙江长征职业技术学院基础部杭州 310023|
3.山东大学威海分校数学与统计学院山东威海 264209

收稿日期:2012-03-06 修回日期:2013-04-19 出版日期:2013-08-25 发布日期:2013-08-25
基金资助:
山东省自然科学基金(Y2008A02)和河北省张家口市2010年第一批市科学技术研究与发展指导计划项目(1021006B)资助.

The Discuss about B.M.Brown et al' Open Problem

JING Hai-Bin¹, WANG Xin-Zhen², QI Jian-Gang³

1.Department of Mathematics and Physics, Hebei Institute of Architecture and Civil Engineering, Hebei Zhangjiakou 075000|2.Basic Department, Zhejiang Changzheng Professional and Technical College, Hangzhou 310023|3.Faculty of Mathematics and Statistics, Shandong University at Weihai, Shandong Weihai 264209

Received:2012-03-06 Revised:2013-04-19 Online:2013-08-25 Published:2013-08-25
Supported by:
山东省自然科学基金(Y2008A02)和河北省张家口市2010年第一批市科学技术研究与发展指导计划项目(1021006B)资助.

摘要/Abstract

摘要：

利用对称Hamilton微分系统的极限点、极限圆分类理论,给出了复系数奇异Sturm-Liouville方程的Sims分类:极限点1型、极限
点2型和极限圆型;并且对B.M.Brown等人提出的开问题进行了详细的讨论.

关键词: 奇异Sturm-Liouville方程, 极限点(圆)型, 复系数

Abstract:

By using limit-point(circle) classification theory of symmetric Hamiltonian differential systems, the paper firstly gives the Sims-classification of singular Sturm-Liouville equations with complex coefficients: limit-point-1 case, limit-point-2 case and limit-circle case. Furthermore, the paper in detail gives a discussion to the open problem of B.M.Brown et al.

Key words: Singular Sturm-Liouville equations, Limit-point(circle) case, Complex coefficients

中图分类号:

34B24

景海斌, 王欣阵, 綦建刚. 对B.M.Brown等人提出的开问题的探讨[J]. 数学物理学报, 2013, 33(4): 709-718.

JING Hai-Bin, WANG Xin-Zhen, QI Jian-Gang. The Discuss about B.M.Brown et al' Open Problem[J]. Acta mathematica scientia,Series A, 2013, 33(4): 709-718.